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The annual incomes of a sample of middle-management employees at Westinghouse are $62,900, $69,100, $58,300, and $76,800.
- (a) Give the formula for the sample
mean . - (b) Find the sample mean.
- (c) Is the mean you computed in (b) a statistic or a parameter? Why?
- (d) What is your best estimate of the population mean?
(a)
Mention the formula for the sample mean.
Answer to Problem 1.1SR
The formula for sample mean is
Explanation of Solution
Sample mean:
The sample mean is the sum of all data values in the sample, divided by total number of data values from the sample. The formula for sample mean is,
In notations the formula for sample mean is,
In the formula,
(b)
Find the sample mean for a sample of annual incomes of middle-management employees at Westinghouse.
Answer to Problem 1.1SR
The sample mean for a sample of annual incomes of middle-management employees at Westinghouse is $66,775.
Explanation of Solution
Calculation:
The number of data values in the sample is 4.
Add all values of sample for ‘
Hence, the sample mean for a sample of annual incomes of middle-management employees at Westinghouse is $66,775.
(c)
Identify whether the mean is a statistic or parameter.
Answer to Problem 1.1SR
The mean calculated is a statistic as it is calculated for the sample values.
Explanation of Solution
Parameter:
The characteristic that is measurable for a population in the study is denoted as parameter.
Statistic:
The characteristic that is measurable for a sample in the study is denoted as statistic.
The mean is calculated for a sample of annual incomes middle-management employees at Westinghouse. Since mean is calculated for the sample data values it would represent the measurable characteristic for the sample. This shows that, the mean calculated is a statistic.
Hence, the mean calculated is a statistic as it is calculated for the sample values.
(d)
Find the best estimate of the population mean.
Answer to Problem 1.1SR
The best estimate of the population mean is sample mean value $66,775.
Explanation of Solution
The best estimate for any population is its sample. Thus, the best estimate for the population mean would be its sample mean.
The sample mean for annual incomes of middle-management employees at Westinghouse is $66,775. The value $66,775 would be the best estimate for population mean.
Hence, the best estimate of the population mean is sample mean value $66,775.
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Chapter 3 Solutions
Statistical Techniques in Business and Economics
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